rizer.transport.heat_loss#

Conductive heat loss of a cylindrical plasma column to its wall.

A volumetric loss term for the 0D reactors’ energy balances, evaluated on a Cantera plasma object at its current state. Every geometric and boundary quantity (column radius, wall temperature) is an explicit argument – nothing is defaulted here.

Functions#

thermal_conductivity(→ float)

Return the thermal conductivity of the plasma in W/m/K.

conductive_heat_loss(→ float)

Return the conductive heat loss per unit volume of the plasma in W/m^3.

Module Contents#

rizer.transport.heat_loss.thermal_conductivity(plasma: cantera.Solution, T_ext: float) → float#

Return the thermal conductivity of the plasma in W/m/K.

The mixture thermal conductivity is computed using [Mathur1967] formula, at the average of the gas temperature and the external temperature.

Only the conductivities of H2 and CH4 are available; every other species is treated as CH4, so the result is only accurate for H2/CH4 mixtures.

TODO: Implement the thermal conductivity of other species. TODO: Use https://cantera.org/dev/python/transport.html

Warning

UNREVIEWED PHYSICS (rizer/adaptive_models/PHYSICS.md, section 4.5). The equations above and their implementation have not been validated by a human: do not use results from this closure for design decisions or publication. Open findings: PHY-19.

Reviewed-by: nobody yet – set the class attribute reviewed_by (rizer.adaptive_models.review) to sign off.

Parameters:

  • plasma (cantera.Solution) – Plasma object at the state to evaluate (gas temperature, composition).

  • T_ext (float) – External (wall/ambient) temperature, in Kelvin.

Returns:

Thermal conductivity in W/m/K.

Return type:

float

Notes

The thermal conductivity \(\lambda\) is given by [Mathur1967]:

\[\lambda = \frac{1}{2} \left( \sum_k X_k \lambda_k + \frac{1}{\sum_k X_k / \lambda_k} \right)\]

with:

  • \(X_k\) the mole fraction of species \(k\),

  • \(\lambda_k\) the thermal conductivity of species \(k\).

The per-species conductivities come from the NASA fits of https://ntrs.nasa.gov/api/citations/19950021761/downloads/19950021761.pdf.

rizer.transport.heat_loss.conductive_heat_loss(plasma: cantera.Solution, radius: float, T_ext: float) → float#

Return the conductive heat loss per unit volume of the plasma in W/m^3.

Parameters:

  • plasma (cantera.Solution) – Plasma object at the state to evaluate.

  • radius (float) – Plasma column radius, in meters.

  • T_ext (float) – External (wall/ambient) temperature, in Kelvin.

Returns:

Heat loss in W/m^3.

Return type:

float

Notes

The heat loss is given by (p199 of [Raizer1991], eq. 8 of [Heijkers2020]):

\[q = 8 \cdot \frac{\lambda_{\text{mix}} \cdot (T_{\text{gas}} - T_{\text{ext}})}{r^2}\]

with:

  • \(\lambda_{\text{mix}}\) the thermal conductivity of the mixture (thermal_conductivity()),

  • \(T_{\text{gas}}\) the gas temperature,

  • \(T_{\text{ext}}\) the external temperature,

  • \(r\) the radius of the plasma.